文章基本信息

标题：Sub-computable Boundedness Randomness
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作者：Sam Buss ; Douglas Cenzer ; Jeffrey Remmel 等
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2014
卷号：10
期号：4
页码：1
DOI：10.2168/LMCS-10(4:15)2014
出版社：Technical University of Braunschweig
摘要：This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for PSPACE functions. These new notions are robust in that there are equivalent formulations in terms of (1) Martin-Löf tests, (2) Kolmogorov complexity, and (3) martingales. We show these notions can be equivalently defined with prefix-free Kolmogorov complexity. We prove that one direction of van Lambalgen's theorem holds for relative computability, but the other direction fails. We discuss statistical properties of these notions of randomness.
其他关键词：algorithmic randomness, subcomputable classes, polynomial space, primitive recursive.